Behaviour under cyclic loading of strengthened beams

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Dec 11, 2017 - cíclicas, as vigas que não romperam por fadiga foram submetidas a uma carga estática até a ruptura. As principais variáveis foram a condição.
Volume 10, Number 6 (December 2017) p. 1245 – 1272 • ISSN 1983-4195 http://dx.doi.org/10.1590/S1983-41952017000600007

Behaviour under cyclic loading of strengthened beams Comportamento de vigas reforçadas sob ação de carregamento cíclico



A. P. R. VAZ a [email protected] I. A. E. SHEHATA b [email protected] L. C. D. SHEHATA c [email protected] R. B. GOMES d [email protected]

Abstract This work presents a study on the behavior of reinforced concrete beams strengthened in bending by the addition of concrete and steel on their tension side and having expansion bolts as shear connectors at the junction between the beam and the jacket, subjected to a cyclic loading. The experimental program included tests on six full scale reinforced concrete beams, simply supported, initially with rectangular cross section 150 mm wide and 400 mm high, span of 4000 mm and total length of 4500 mm. All the beams, after receiving two cycles of static loading in order to create a pre-cracking condition, were strengthened in bending by partial jacketing and then subjected to cyclic loading until the completion of 2x106 cycles or the occurrence of fatigue failure. Following the cyclic loading, the beams that did not fail by fatigue were subjected to a static load up to failure. The main variables were the beam-jacket interface condition (smooth or rough), the flexural reinforcement ratio in the beam and in the jacket, and cyclic load amplitude. On the basis of the obtained test results and the results of previous studies of similar beams tested only under static loading, the behavior of the strengthened beams is discussed and a proposal for the beam-jacket connection design is presented, for the cases of predominantly static and cyclic loading. Keywords: flexural strengthening, partial jacketing, fatigue, beams, cyclic loading.

Resumo Este trabalho apresenta estudo sobre o comportamento de vigas de concreto armado reforçadas à flexão, pela adição de concreto e barras de aço na região tracionada e chumbadores de expansão na ligação viga-reforço, submetidas a carregamento cíclico. O programa experimental incluiu ensaios em seis vigas de concreto armado em escala real, simplesmente apoiadas, inicialmente com seção transversal retangular com 150 mm de largura e 400 mm de altura, comprimento entre os apoios de 4000 mm e comprimento total de 4500 mm. Todas as vigas, depois de receber dois ciclos de carga estática, de modo a criar uma condição de pré-fissuração, foram reforçadas à flexão por encamisamento parcial e, em seguida, submetidas a uma carga cíclica até ao final de 2x106 ciclos ou da ocorrência de ruptura por fadiga. Após a aplicação das cargas cíclicas, as vigas que não romperam por fadiga foram submetidas a uma carga estática até a ruptura. As principais variáveis foram a condição de interface de ligação entre viga e reforço (lisa ou rugosa), a taxa de armadura de flexão na viga e no reforço, e amplitude do carregamento cíclico. Com base nos resultados obtidos nos ensaios e em estudos anteriores de vigas semelhantes testadas apenas com carga estática, é feita uma discussão do comportamento dessas vigas reforçadas e apresentada uma proposta para dimensionamento da ligação viga-reforço, para os casos de carregamento predominantemente estático e cíclico. Palavras-chave: reforço à flexão, encamisamento parcial, fadiga, vigas, concreto armado.

a



d b c

Saneamento de Goiás S/A, Departamento de Estruturas, Goiânia, GO, Brasil; COPPE, Universidade Federal do Rio de Janeiro, Programa de Engenharia Civil, Rio de Janeiro, RJ, Brasil; Universidade Federal Fluminense, Departamento de Engenharia Civil, Niteroi, RJ, Brasil; Universidade Federal de Goiás, Departamento de Engenharia Civil, Goiânia, GO, Brasil.

Received: 25 Aug 2016 • Accepted: 23 Mar 2017 • Available Online: 11 Dec 2017

© 2017 IBRACON

Behaviour under cyclic loading of strengthened beams

1. Introduction Strenghtening reinforced concrete beams by adding concrete and steel bars presents the advantages of relatively low cost and no need for a highly qualified workforce, making it an interesting alternative when it is possible to increase the cross-section dimensions of the element to be strengthened. The effectiveness of strenghtening by jacketing relies on the efficiency of the connection between the beam and the jacket. The roughness and cleanness of the surface that will receive the new concrete are essential factors for that efficiency. According to [2], the shear strength of an interface between two concretes increases with increasing roughness. It is a consensus that an adequate curing of the new concrete is needed in order to minimize its initial shrinkage and ensure good bonding between concretes of different ages [3] and there is evidence that interfaces with greater roughness have shear strength less affected by differential shrinkage of the two concretes [4]. The shear strength of the interface between the two concretes can be increased with the use of reinforcement crossing it in two ways: dowel action, which corresponds to the flexural strength combined with axial tension, and by the production of normal stress at the interface, which is an indirect effect mobilized by the relative displacement between the joint. In case of cyclic loading, increasing the ratio of this reinforcement not only decreases the interface damage resulting from such loading, minimizing the loss of stiffness of the strengthened element, but also increases the number of cycles it can withstand. One of the main factors that can reduce the interface shear strength is the effect of cyclic actions, which cause a decrease in the stiffness of the element, associated to a greater propagation of cracks, leading to strains in the structural elements larger than those verified under short-term static loading, and to different stress redistribution. In view of this, beams that, under static loading exhibit flexural failure, when subjected to cyclic loading, can present shear failure or failure by loss of bond between concrete and reinforcement [5]. It should be noted that the number of cycles the structure supports, as well as the degree of interface damage,

is directly related to the amplitude of the cyclic loading to which the structure is subjected. Although conventional reinforcement, which is attached to the element to be strengthened by means of adhesives, is usually used in practice, in this work, the use of the expansion bolts was chosen due to its easier fixation, without adhesives, leading to greater speed in the execution of strengthening. Literature review carried out by Vaz [1] shows that there is not much research on the behavior of strengthened reinforced concrete beams by addition of concrete and steel bars and, among the researches reviewed, the ones described in [7], [8], [9], [10], [11] can be cited. From them, only one included beams with cyclic loading [8] and two included beams with expansion bolts at the beamjacket connection ([10], [11]). In view of the practicality of using expansion bolts at the beam-jacket connection, an experimental study was developed aiming to contribute to the understanding of the behavior of beams strengthened with this technique when they are subjected to cyclic loading. This study, detailed in [1], is summarized here.

2. Experimental program 2.1 Characteristics of the beams and test methods The main variables of the 6 tested beams were: n ratio of tensile longitudinal reinforcement of the beams before (1,09% or 0,483%) and after strengthening (0,401%, 0,541%, 1,00% or 1,31%); n the beam-jacket interface condition (rough or smooth); n the cyclic load amplitude. The beams with no strengthening had rectangular cross-sections 150mm wide and 400mm high and a total length of 4500mm. The beams were simply supported, with a distance of 4000mm between the centers of the supports (one roller and one pinned). The concentrated loading was applied at midspan. The beams were designed to have flexural failure, with yielding of longitudinal tensile steel, having sufficient transversal reinforcement to guarantee such a failure. Figure 1 and table 1 show the dimensions and reinforcement of the beams before strengthening.

Figure 1 Geometrical characteristics of beams before strengthening

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A. P. R. VAZ | I. A. E. SHEHATA | L. C. D. SHEHATA | R. B. GOMES

Table 1 Dimensions and reinforcement of the beams before strengthening Beam

b (mm)

h (mm)

d (mm)

d’ (mm)

As (mm2)

r (%)

As’ (mm2)

r’ (%)

Asw/S (mm2/ mm)

rsw (%)

V1 and V2

150

400

369

27

603

1.09

100

0.182

0.670

0.447

V3 to V6

150

400

386

27

280

0.483

100

0.174

0.670

0.447

Asw – cross-section area of shear reinforcement in length s; s – spacing of shear reinforcement; As – cross section area of longitudinal tensile reinforcement; As´ – cross section area of longitudinal compression reinforcement; r – geometrical ratio of longitudinal tensile reinforcement; r’– geometrical ratio of longitudinal compression reinforcement; rsw – geometrical ratio of transverse reinforcement.

Before strengthening, the beams were pre-cracked. This procedure consisted in the application of static loading at the middle of the span until the strains of the bending reinforcement at midspan were around 2.0 ‰. Next, the beams were unloaded, and prepared to be strengthened. On the lateral faces of the regions that would become beam-jacket interfaces, the surface concrete was removed (depth about 15mm) using a chisel, exposing the reinforcement (tensile longitudinal and transverse) and coarse aggregates. On the lower face, where, in practice, this would be more difficult to do, the cover was not totally removed and the surface was only chipped to make it rough. This procedure was used for beams V1R to V4R, while for beams V5R and V6R the beam surface was left as it was (smooth). Although more sophisticated methods can be used in laboratory ([12] and [13]), the roughness index R was measured by the sand

patch method. After roughening the lower surface of the beams, this method was used in three different regions along the lengths of the beams. Table 2 gives the values of R found and their mean Rm. For cases with R ≥ 1,5mm, according to [13], the surface can be classified as rough. The strengthening consisted of a reinforced concrete jacket with a trapezoid-shaped cross-section, geometrically equal to the one used in beams of previous work ([10] and [11]), exempt that the width of the lower part of the V5R and V6R jacket measured 180mm instead of 150mm. This difference in V5R and V6R was due to the fact that, prior to strengthening, no concrete surface layer was removed from these beams in the region that would be the beam-jacket interface. On the sides of the that region, 9.5 mm diameter expansion bolts similar to those used by Santos [10] and Simões [11] were installed,

Figure 2 Expansion bolts Table 2 Roughness index R values and their mean Rm Beam

R (mm)

Rm (mm)

Beam

1.50 V1

V2

1.52

R (mm) 1.52

1.54

V3

1.55

1.59

1.56

1.57

1.47

1.59 1.49

IBRACON Structures and Materials Journal • 2017 • vol. 10 • nº 6

Rm (mm)

1.55

V4

1.58

1.54

1.52

1.52

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Behaviour under cyclic loading of strengthened beams and with the same 150mm spacing (figure 2). They served both for positioning the jacket reinforcement and improving the performance of the beam-jacket connection. The ratio of expansion bolts in the beam-jacket connection (rw) was 0.329% for beams with rough surface and 0.298% for those with smooth surface (larger beam-jacket interface area). Considering the yield stress of expansion bolts of the 540MPa, leads to rwfy values of 1.78 MPa or 1.61 MPa for rough and smooth surface, respectively. Figure 3 gives details of the reinforcement in the jackets and Table 3 the reinforcement of the strengthened beams of this study and of similar beams of previous works ([10] and [11]).

After about 30 days from casting the jackets, cyclic loading was started, with a frequency of 2Hz or 3 Hz and loads ranging from about 25% to 50%, 30% to 60% or 35% to 70% of the theoretical bending failure load. The beams were subjected to cyclic loading until the occurrence of fatigue failure or completion of a total number of 2x106 cycles. The beams that resisted to 2x106 loading cycles, without having a fatigue failure, were unloaded and, then, subjected to a final static load up to failure. For testing, the beams were simply supported (one roller and a pinned support) having a span of 4000mm. They were loaded at mid-span using a 500kN capacity jack connected to a load/displacement control system.

Figure 3 Reinforcement in the jackets of beams V1R to V6R Table 3 Dimensions and reinforcement of the strengthened beams Current work Main steel (f in mm)

dR

As (mm2)

AsR (mm2)

rR (%)

rT (%)

Beam

Jacket

V1R

3f16,0

4f6,3 and 2f8,0

374

603

225

0.401

1.48

V2R

3f16,0

6f8,0

372

603

302

0.541

1.62

V4R

2f10,0 and 1f12,5

4f8,0 and 2f16,0

402

280

603

1.00

1.47

V3R, V5R, V6R

2f10,0 and 1f12,5

4f8,0 and 3f16,0

409

280

804

1.31

1.77

dR

As (mm2)

AsR (mm2)

rR (%)

rT (%)

Earlier works Main steel (f in mm) Beam

Jacket

VR1 [10]

3f16,0

6f8,0

372

603

302

0.541

1.62

VR2 [11]

2f10,0 and 1f12,5

4f8,0 and 2f16,0

402

280

603

1.00

1.47

VR3 [11]

2f10,0 and 1f12,5

4f8,0 and 3f16,0

409

280

804

1.31

1.77

b = 150mm; h = 470mm; d´= 27mm; As´= 100mm2 Stirrups (jacket): f5,0 c/150 mm

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A. P. R. VAZ | I. A. E. SHEHATA | L. C. D. SHEHATA | R. B. GOMES During the static loading tests, concrete strains were measured at four levels of a section at 130mm from the midspan (figure 4), by means of a demec gauge with 100 mm length gage and a smaller division of 0.001mm. Strains of the longitudinal tensile reinforcement were measured using electrical resistance strain gauges

stuck on the bars of the beams and the jackets, at midspan and at a section 960mm from midspan (figure 5). The vertical displacements of the beams were measured using two strain gauge displacement transducers, at sections 150mm apart from the midspan and at each side of the loading region. The relative horizontal

Figure 4 Position of bases for demec gauge measurements

Figure 5 Cross-section of strengthened beams and strain gauges positions on longitudinal tensile reinforcement of the jackets

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Behaviour under cyclic loading of strengthened beams displacements at the beam-jacket connection were measured with strain gauge displacement transducers placed at the section at 960mm from midspan and at the end of the jacket using aluminium devices (figure 6).

2.2 Materials CA-50 and CA-60 steel bars were used as reinforcements of beams and jackets. The transverse reinforcement of the beams and of the jackets had 8.0 mm and 5.0 mm diameter, respectively. The longitudinal compression reinforcement of the beams consisted of 8.0 mm diameter bars, as well as the longitudinal reinforce-

ment of jackets together with 6.3 mm bars. The longitudinal tensile reinforcement of beams V1 and V2 and some of the jackets had 16.0 mm diameter. Bars of 10.0 mm and 12.5 mm diameter were used as longitudinal tensile reinforcement of beams V3 and V6. Samples of each type of bar were tested and the average values of yield stress and tensile strength obtained were, respectively, 655 MPa and 739 MPa (5.0 mm), 596 MPa and 767 MPa (6.3 mm), 607 MPa and 748 MPa (8.0 mm), 522 MPa and 641 MPa (10.0 mm), 555 MPa and 688 MPa (12.5 mm), 562 MPa and 686 MPa (16.0 mm). The concrete mix was chosen aiming a compressive strength of 30 MPa at 28 days. For each concrete batch cylindrical specimens

Figure 6 Position of displacement transducers for measurement of relative longitudinal displacements between beam and jacket

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A. P. R. VAZ | I. A. E. SHEHATA | L. C. D. SHEHATA | R. B. GOMES were moulded for the compression, tensile and modulus of elasticity tests. The mean values obtained in the tests related to concretes of the beams and jackets were, respectively: 34.0 MPa and 33.0 MPa for compression strength, 3.60 and 3.57 MPa for splitting tensile strength and 26.0 GPa for modulus of elasticity.

3. Results and discussion Table 4 summarizes the experimental results of the tested beams. The theoretical bending failure load values of the strengthened beams, Pu,theo, used in this table were determined using fc and fy obtained in the material tests (gc=gs=1) and are given in table 5.

3.1 Cracks and load In the strengthened beams, some cracks on the jackets were observed during the two static loading cycles before the cyclic loading. During the cyclic loading, other flexural cracks appeared in the jacket up to about the first 100 000 cycles for the beams V1R, V2R, V3R and V5R, 70 000 cycles for the V4R and 5000 cycles for the V6R. Besides theses cracks, in V4R and V6R, with a load variation between 25% to 50% of Pu,theo and higher rRfy values (5,69MPa and 7,39MPa), shear cracks appeared in the regions near the supports and horizontal cracks in the beam-jacket connection. Beam V6R, that failed by fatigue of the expansion bolts at beam-jacket

Table 4 Loading and results of the tested beams Initial static loading (before strengthening) Beam

rR (%)

rT (%)

Pcr (kN)

Pmax (kN)

δi (mm)

εs,i (‰)

εs,ires (‰)

δres,i (mm)

V1 V1R

0.401

1.48

25

60

8.73

1.78

0.383

2.31

V2 V2R

0.41

1.62

25

60

8.88

1.72

0.368

2.00

V3 V3R

1.31

1.77

20

35.4

8.58

1.99

0.527

2.43

V4 V4R

1.00

1.47

15

35.3

8.96

2.09

0.602

2.95

V5 V5R

1.31

1.77

20

35.6

7.66

2.08

0.497

2.09

V6 V6R

1.31

1.77

20

35.5

7.68

1.97

0.481

2.15

Cyclic loading (strengthened) Pmin/Pu,teo (%)

Beam

Pmax/Pu,teo (%)

εs,max (‰)

εs,res (‰)

δres (mm)

V1 V1R

33

64

2.36





V2 V2R

19

40

1.28

0.352

1.74

V3 V3R

22

42

1.57

0.345

2.52

V4 V4R

24

58

1.64



4.54

V5 V5R

21

42

1.37

0.301

2.21

V6 V6R

27

54

1.49





Final static loading (strengthened) Pu,exp (kN)

δu,exp (mm)

V1 V1R



V2 V2R

193

Beam

Maximum relative displacement (mm)

εsu,exp (‰)

Failure mode

Beam

Jacket

S1

S2

S3













33.8

46.7

50.52



0.081

0.058

Flexure Shear at beamjacket interface

Steel fatigue 1.865.825 cycles

V3 V3R

180

18.1

2.24

2.59

0.754

0.051

9.85

V4 V4R

186

25.3





0.641

0.04

0.444

Flexure

V5 V5R

173

28.6

2.02

2.20

1.34

0.843

6.57

Shear at beamjacket interface

V6 V6R















Bolts fatigue 875.280 cycles

ρR – tgeometric ratio of longitudinal tensile reinforcement of jacket; ρT – total geometric ratio of longitudinal tensile reinforcement of strengthened beam; δi – vertical displacement corresponding to the maximum load Pmax in the initial static test; δres,i – residual vertical displacement at the end of the initial static test; δres – residual vertical displacement at the end of cyclic loading; δu,exp – vertical displacement at failure load of beams that did not have fatigue failure; εs,i – longitudinal reinforcement strain of the beam corresponding to the maximum load in the initial static test; εs,res – residual strain of longitudinal reinforcement of the beam at the end of initial static test; εs,max – maximum strain of longitudinal reinforcement of the beam during cyclic loading; εu,exp – maximum strain of longitudinal reinforcement of the beam or jacket at failure load of the beams that did not have fatigue failure; Pcr – load corresponding to the first visible cracks during initial static test; Pu,exp – experimental failure load of the beams that did not have fatigue failure.

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Behaviour under cyclic loading of strengthened beams

Table 5 Experimental and theoretical failure loads of strengthened beams of [1] and previous work [10] and [11] Static loading Rough beamjacket interface Beams

rR (%)

rT (%)

V1R

0.401

1.48

2.29

VR1 [10]

0.541

1.62

V2R

0.541

1.62

VR2 [11]

1.00

V4R

rRfy rTfy (MPa) (MPa)

Cyclic loading Rough beamjacket interface

Cyclic loading Smooth beam-jacket interface

Pu,exp (kN)

Pu,teo (kN)

Pu,exp/ Pu,teo

Pu,exp (kN)

Pu,teo (kN)

Pu,exp/ Pu,teo

8.46













2.97

8.92

186

156

1.19













3.12

9.33







193

168

1.15







1.47

6.11

8.98

205

192

1.07













1.00

1.47

5.69

8.29







186

177

1.05







VR3 [11]

1.31

1.77

8.29

10.8

229

230

1.00













V3R

1.31

1.77

7.39

9.98







180

212

0.85







V5R

1.31

1.77

7.39

9.98













173

216

0.80

1.31

1.77

7.39

9.98













V6R Flexure

Shear at the beam-jacket interface

Pu,exp (kN)

Pu,teo (kN)

Pu,exp/ Pu,teo

Steel fatigue

Bolts fatigue

Fatigue

connection, presented the greatest number of shear cracks during the cyclic loading. In V1R, with lower longitudinal reinforcement ratio in the jacket (rRfy=2,29MPa) and a load variation between 32% and 64% of Pu,theo, these horizontal and shear cracks did not appear. It had failure by fatigue of the main steel of the jacket and showed only bending cracks and with greater width. During the final static test, beams V2R and V4R, that had bending failure, presented similar cracking patterns. The beams V3R and V5R, which had shear failure at the beam-jacket connection, presented smaller number of flexural cracks than the other beams. The theoretical and experimental values of bending strength of the strengthened beams of this and previous researches ([10] and [11]), calculated with experimental values of concrete compressive strength and steel yield stress and parabola-rectangle diagram for normal compression stresses in concrete, are presented in table 5. The experimental maximum values of normal stresses and the variation of these stresses in the longitudinal tensile reinforcement at the beginning of cyclic loading, obtained from the measured

steel strains, and also the calculated ones are given in table 6. Table 5 shows that only the beams of this study that had shear failure at the beam-jacket connection had a ratio smaller than one (0.85 and 0.80) and that the beam with the smooth beam-jacket interface had the lowest ratio. For the beams of previous work [11] similar to those of this study, but subjected to a static loading only, with shear failure at the beam-jacket connection, this ratio was 1.07 and 1.00. Comparing V3R with VR3 [11] (rT = 1.77% and rR = 1.31%, with rough beamjacket interface and shear failure at this connection), it is found that the V3R had a resistance capacity 21% smaller. However, this reduction cannot be attributed only to cyclic loading, since V3R had rRfy 11% lower. Taking this into account, the reduction of strength due to cyclic loading becomes 12%. In beams with rT = 1.62% and rR = 0.541% (V2R of this study and VR1[10]), which had bending failure, the cyclic loading did not affect the resistance capacity, since the difference between the experimental failure loads of beams with only static loading and with

Table 6 Maximum normal stresses and variation of these stresses in the longitudinal tensile reinforcement at the beginning of cyclic loading, obtained from measured and calculated steel strains Beams V1R

rTfy rRfy (MPa) (MPa) 2.29

8.46

Pmin/ Pu,teo (%)

Pmáx/ Pu,teo (%)

σs,max (MPa)

σs,max,calc (MPa)

Δσs (MPa)

Δσs,calc (MPa)

32

64

299

366

155

183

σsR,max σsR,max,calc (MPa) (MPa) 477

494

ΔσsR (MPa)

ΔσsR,calc (MPa)

231

247

V2R

3.12

9.33

20

40

187

234

100

117

225

317

102

159

V4R

5.69

8.29

25

56

265

304

152

167

330

380

174

209

V3R

7.39

9.98

21

42

172

213

87

107

253

269

116

135

V5R

7.39

9.98

21

42

173

213

98

107

225

269

111

135

V6R

7.39

9.98

27

54

227

275

130

137

293

347

157

174

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A. P. R. VAZ | I. A. E. SHEHATA | L. C. D. SHEHATA | R. B. GOMES static loading after the cyclic one corresponds almost to the difference between the values of rTfy of these beams. The V1R (rT = 1.48% and rR = 0.401%) had the highest Pmin/Pu,theo and Pmax/Pu,theo ratios of the tested beams (32% and 64%) and, consequently, larger variations of normal stress in the reinforcement in the jacket (causing fatigue in that reinforcement) and of vertical displacement. This beam had ssR,max= 477MPa ≈ 0,79 fy and DssR=231MPa. In figure 7, it can be seen that, for the number of cycles verified in V1R (1 865 825), there was a variation of normal stress in the reinforcement greater than the limit given by the relationship between Dss and the number of cycles N of ABNT NBR 6118:2014 [14]. Due to the low steel ratio used in the jacket, the shear stress variation at the beam-jacket interface was low and there was no slipping at that connection.

3.2 Reinforcement strains For the static load before the cyclic one, in general, the ratios between the strains of the reinforcement in the jacket (bottom layer) and in the beam varied between 1.2 and 1.4, values that would be expected according to a state II analysis, but in beam V1R these ratios ranged from 1.5 to 1.7. During cyclic loading, except for V2R, the measured maximum and minimum strains of the longitudinal tensile steel, as a function of number of cycles, for beams that did not have fatigue failure did not show a stabilization tendency. Beam V6R, that had fatigue failure of the expansion bolts, had a differentiated behavior, presenting a sudden decrease in the strains of the longitudinal reinforcement of the jacket and, at the same time, a sudden increase in the strains of the longitudinal reinforcement of the beam, when N was equal to about 600 000 cycles (figure 8). Table 7 lists the values of the maximum strains of the longitudinal tensile reinforcement of jackets and beams measured during cyclic loading, as well as the variation of these strains and the residual strains at the end of loading. These values depend on Pmin ⁄ Ptheo and Pmax ⁄ Ptheo and on rT. The strains of longitudinal reinforcement in the jacket measured during the final static loading at midspan of V2R are compared with the ones of beam VR1[10] in figure 9, and those of beams V3R and V5R compared with the ones of V3R [11] in figure 10. The curves of beams VR1[10] and V2R are practically coincident for load values up to 50kN; for higher loads, the curve of V2R, with ρTfy about 5% higher, show smaller strains. In figure 10, it can be seen that, for the same load, beam V5R, with smooth beam-jacket interface, presented smaller strains than

Figure 7 Comparison between the relationship between N and DssR according to ABNT NBR 6118:2014 [14] and the one of the beam with steel fatigue failure V3R, with rough surface, and that the strains curve of V3R is close to that of VR3 [11], and although the two beams had the same kind of failure, the excessive slipping at the beam-jacket interface of V3R prevented the longitudinal reinforcement of the jacket from having strains higher than εy* (strain corresponding to fy when a steel bilinear normal tensile stress-strain diagram with plateau is considered) and caused V3R to fail at a lower load than VR3 [11], for which strains larger than the yielding one were measured (about 8.5‰).

3.3 Longitudinal force, shear stress and slipping at the beam-jacket connection The longitudinal force TR, and, from it, the shear stress at the beamjacket interface t, was calculated using the strains measured in the longitudinal reinforcement of the jacket at midspan. Table 8 shows TR,max and DTR during cyclic loading, obtained from measured and calculated strains. The sum of the jacket longitudinal reinforcement forces at midspan of each beam obtained from the measured strains, for different levels of the final static loading, is in table 9 and figure 11 gives these longitudinal forces as a function of the applied load for beams V3R, V5R and V6R, together with the ones of VR3 [11], with the same tensile longitudinal reinforcement ratio. This figure shows the variation that the measured strains may have as a result of cracking, since, from equilibrium condition at

Figure 8 Maximum main steel strain of jacket and beam, at midspan, as a function of the number of cycles of beams with same reinforcement ratio, with rough (V3R) and smooth interface (V5R and V6R)

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Table 7 Maximum strain of the longitudinal tensile reinforcement of jacket and beam and strain variation during cyclic loading and residual strain at the end of loading Beam

rR (%)

rT (%)

Pmin/ Pu,teo (%)

Pmax/ Pu,teo (%)

εsR,max (‰)

ΔεsR (‰)

εsR,res (‰)

εs,max (‰)

Δεs (‰)

εs,res (‰)

V1R

0.401

1.48

32

64

2.36+

1.15+



1.49+

0.777+



V2R

0.541

1.62

20

40

1.28

0.532

0.352

1.04

0.539

0.244

V4R

1.00

1.47

25

56

1.64+

0.863+



1.41+

0.842+



V3R

1.31

1.77

21

42

1.57

0.576

0.345

1.09

0.501

0.235

V5R

1.31

1.77

21

42

1.37

0.769

0.301

1.08

0.579

0.229

V6R

1.31

1.77

27

54

1.49*

0.836*



1.24*

0.781*



+ < 100.000 cycles | * 600.000 cycles

midspan, for a given load, beams with same longitudinal steel ratio must have the same value of TR. Table 10 lists the values of horizontal force at the beam-jacket connection (static loading) and the variation of that force during cyclic loading for beams that had shear failure at the beam-jacket connection, and also for V4R. On the basis of the TR,max and DTR values for beams V5R and V6R given in table 10, and considering that the longitudinal force at beam-jacket connection is resisted only by the expansion bolts (24 bolts in all, disregarding the two bolts at midspan), the equations (1.0a) and (1.0b) that give the expansion bolt shear force variation, DTR,ch, as a function of the number of cycles could be deduced. The one that gives logDTR,ch as a function of logN (1.0a) is of the type commonly used for shear connectors [15] and the one that gives DTR,ch as a function of logN (1.0b) is its equivalent. The same expression was assumed for smooth and rough interfaces, in view of the little difference between the strengths of beams V3R and V5R, and TR,ch is given in newtons.

(1a)

Figure 9 Load - maximum longitudinal steel strain curves for beams VR1 [10] and V2R

1254

or

(1b) These expressions can be written in the form of shear stress variation in the bolts (in MPa), that is

(2a) or

(2b) It should be noted that, for N=1, this variation is approximately equal to 0.4fy and that, according to Tresca failure criteria (which is more conservative than the Von Mises one), the shear stress limit would be 0.5fy. This lower resistance can be explained by the stress concentration due the existence of thread in the expansive bolts and by the fact that the expansive bolts are not subjected to pure shear.

Figure 10 Load - maximum longitudinal steel strain curves for beams VR3 [11], V3R and V5R

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A. P. R. VAZ | I. A. E. SHEHATA | L. C. D. SHEHATA | R. B. GOMES

Table 8 Jacket main steel maximum force TR,max and force variation DTR under cyclic loading, obtained from measured and calculated steel strains rT (%)

rR (%)

Beam

Pmin (kN)

Pmax (kN)

TR,max (kN)

TR,max,calc (kN)

DTR (kN)

TR,max,calc/ TR,max

DTR,calc (kN)

DTR,calc/ DTR

V1R

2.29

8.46

50

100

79.2

89.8

1.13

40.2

44.8

1.11

V2R

3.12

9.33

34

68

58.0

73.1

1.26

30.4

36.5

1.20

V4R

5.69

8.29

45

100

186

201

1.08

102

111

1.09

V3R

7.39

9.98

45

90

179

196

1.10

84.6

98.2

1.16

V5R

7.39

9.98

45

90

167

196

1.18

87.2

98.2

1.13

V6R

7.39

9.98

58

116

218

253

1.16

120

127

1.06

Figure 12 shows the relationship between the shear resistance at the connection, τR, and ρw fy given by the expression tR = 0,4 ρw fy and those of beams VR2 and VR3 of [11] and V3R and V5R. All of them had longitudinal shear failure at the beamjacket interface during monotonically increasing load, but VR2 and VR3 [11] had not been previously subjected to cyclic loading. Beam V4R was also included, although it had bending failure, because shear failure at the beam-jacket connection was imminent. The τR values of V4R, V3R and V5R are those of residual shear strength after cyclic loading. This figure shows that, with the exception of V4R, which did not have failure at the beam-jacket connection, the expression tR = 0,4 ρw fy leads to values of τR smaller than or approximately equal to the ones of the beams analyzed, for both beams tested only statically and for those subjected to cyclic loading before the static one (residual resistant shear stress). Figures 12 and 13 suggest that the beam-jacket connections provided with expansion bolts can be designed considering

Figure 11 Load - TR curves of beams VR3 [11], V3R, V5R and V6R, with same reinforcement ratio

(3)

e

frequent variable loads) and minimum (permanent loads), respectively, and fyd = fy ⁄ 1,15. The maximum displacements between beam and jacket, in the

where N is the expected loading cycles, Dt is obtained from the longitudinal forces values at the connection TRmax and TRmin calculated at stage II, for maximum service load (permanent loads +

Table 9 Longitudinal force and nominal shear stress at the beam-jacket interface during final static loading τ (MPa)

TR (kN)

Load (kN)

V1R+

V2R

V4R+

V3R

V5R

V6R

V1R+

V2R

V4R+

V3R

V5R

V6R+

0

0

0

0

0

0

0

0

0

0

0

0

0

20

8.83

17.9

30.7

33.2

19.1

36.3

0.017

0.0330

0.0571

0.0618

0.0321

0.0611

40

26.3

36.3

70.6

75.2

48.5

73.9

0.049

0.0680

0.131

0.140

0.0814

0.124

60

43.6

56.0

110

120

92.2

110

0.081

0.104

0.206

0.224

0.155

0.186

80

60.0

72.2

151

163

125

150

0.112

0.134

0.282

0.305

0.210

0.252

100

71.5

82.4

185

202

162

190

0.133

0.153

0.346

0.376

0.272

0.320

120



104



244

202

234



0.194



0.454

0.339

0.395

140



133



291

241





0.247



0.541

0.405



150



142



315

262





0.267



0.586

0.439



160



144



335

290





0.299



0.624

0.487



170



161



356

333





0.299



0.662

0.561



173



161



361

335





0.299



0.673

0.563



180



161



383







0.299



0.712





193



161











0.299









+ static loading before cyclic loading (beams with failure during cyclic loading and V4R, where there was damage in the strain gauges)

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Table 10 Values of TR,max and DTR corresponding to static and cyclic loading Only static loading

During cyclic loading

Static load after cyclic

Beam

rR (%)

rT (%)

TR,max (kN)

DTR (kN)

TR,max*(kN)

VR2 [11]

1.00

1.47

370





V4R

1.00

1.47



VR3 [11]

1.31

1.77

V3R

1.31

1.77

V5R+

1.31

V6R

1.31

+

+

ssmooth interface; TR,max* after cyclic;

++

++

348

490







98.2++

401

1.77



98.2++

385

1.77



127



no failure during cyclic loading;

111

+

+

beams V2R and V4R, that had bending failure, were 0.260 mm and 0.641 mm, respectively. In beams V3R and V5R, with shear failure at the beam-jacket connection, displacements of 0.754 mm and 1.34 mm were registered in the position S1 and 9.85 mm (V3R) and 6.57 m (V5R) in the position S3. Figure 14 shows the relationship between load and slipping at the beam-jacket connection of beams VR3 [11] and V3R and V5R, where plateaus indicate the effect of the expansive bolts used in the connection. Observing in figure 14 the curves of beams with rough beam-jacket interface, V3R, and VR3 [11], it can be seen that, for the same relative displacement value, VR3 [11], which had no cyclic loading, had a higher load.

4. Conclusions There are few experimental studies on shear strength of concrete connections under cyclic loading and, in the literature review [1], no study on connections with expansion bolts was found. According to the MC 2010 (FIB, 2013), in the design of interfaces subjected to

fatigue failure with 875.280 cycles.

cyclic loading, it is recommended a reduction to about 40% of the static resistance, if cracks are likely to occur at the connection. In view of the advantages of the bending strengthening by adding concrete and steel bars and expansion bolts at the beam-jacket connection, the experimental study described here was developed aiming to investigate the behavior of beams strengthened according to this technique, under unidirectional cyclic loading with different amplitudes. The comparison between similar strengthened beams, with rough beam-jacket interface, tested only statically with those that had cyclic loading before the static one showed that cyclic loading had no negative influence on the strength capacity of beams with bending failure (V2R, V4R). The beams with shear failure at the beam-jacket connection, unlike the similar ones tested under only static loading, the larger relative displacements verified at the beam-jacket connection of the beams tested with cyclic loading prevented the longitudinal tensile reinforcement from having strains larger than that corresponding to the beginning of yielding. From the beams that differed only by

Figure 12 Relationship between τR and ρwfy according to expression τR = 0,4rwfy and those of beams VR2 and VR3 [11] and the residual shear stress of V4R, V3R and V5R

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A. P. R. VAZ | I. A. E. SHEHATA | L. C. D. SHEHATA | R. B. GOMES

Figure 13 Shear stress variation in beam-jacket interface as a function of the number of cycles given by equation (2.0b) the condition of the beam-jacket interface (V3R and V5R), the one with smooth interface had resistance practically equal to the one with rough interface. Tests of strengthened beams and direct shear tests of connections between concretes with expansions bolts previously carried out with no cyclic loading showed that the design of the connections should consider

(4)

was verified that it is possible to consider for shear stress variation at the connections

(5) As far as the beam-jacket relative displacements is concerned, it was verified that, for the same load, beam with cyclic loading has greater displacement than the similar beam with only increasing monotonic loading.

On the other hand, to cover the cases of static and cyclic loads, it

Figure 14 Load - relative displacement at the beam-jacket interface curves of VR3[11], V3R[1] and V5R[1]

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5. References [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]

[15]

VAZ, A. P. R.. Comportamento de vigas reforçadas sob ação de carregamento cíclico. Tese de D. Sc., COPPE/ UFRJ, Rio de Janeiro, RJ, 2012. GOHNERT, M. Horizontal shear transfer across a roughened surface. Cement and Concrete Composites, v. 25, n.3, (Apr), pp. 379-385, 2003. CLIMACO, J. C. T. S.; REGAN, P. E. Evaluation of Bond strength between old and new concrete in structural repairs. Magazine of Concrete Research, v. 53, n.6, (Dec), pp. 377390, 2001. BEUSHAUSEN, H., ALEXANDER, M. G. Bond strength development between concretes of different ages. Magazine of Concrete Research, v. 60, n.1, (Feb), pp. 65-74, 2008. MATTOCK, A. H. Shear transfer in concrete having reinforcement at an angle to the shear plane, ACI Special Publication SP-42, American Concrete Institute, pp. 17-42, 1974. LIEW, S. C., CHEONG, H. K.. Flexural behavior of jacketed RC beams. Concrete International, v. 13, n. 12, (Dec), pp. 43-47, 1991. PIANCASTELLI, E. M. Comportamento do reforço à flexão de vigas de concreto armado, solicitando a baixa idade e executando inclusive sob carga. Dissertação de M. Sc., UFMG, Belo Horizonte, Minas Gerais, 1997. CHEONG, H. K.; MacALEVEY, N. Experimental behavior of jacketed reinforced concrete beams. ASCE Journal of Structural Engineering, v. 126, n. 6, (Jun), pp. 692-699, 2000. BORJA, E. V. Estudo do comportamento de vigas de concreto armado reforçadas à flexão e esforço cortante. Dissertação de M. Sc., UFPE, Recife, Pernambuco, 2001. SANTOS, E. W. F. Reforço de vigas de concreto armado à flexão por encamisamento parcial. Dissertação de M. Sc., COPPE/UFRJ, Rio de Janeiro, RJ, 2006. SIMÕES, M. L. F. Reforço à flexão de vigas de concreto armado por encamisamento parcial. Dissertação de M. Sc., COPPE/UFRJ, Rio de Janeiro, RJ, 2007. SANTOS, P. M. D., JÚLIO, E. N. B. S., SILVA, V. D. Correlation between concrete-to-concrete bond strength and the roughness of the substrate surface, Construction and Building Materials, v. 21, n.8, (Aug), pp. 1688-1695, 2007. FÉDÉRATION INTERNATIONALE DU BÉTON, FIB Model Code for concrete structures 2010, 2013. Lausanne, Switzerland. ASSOCIAÇÃO BRASILEIRA DE NORMAS TÉCNICAS, 2014. ABNT NBR-6118:2014: Projeto de Estruturas de Concreto – Procedimento. Rio de Janeiro, RJ, Brasil. XIE, E., VALENTE, M. I. B. Fatigue strength of shear connectors, Research Report, universidade do Minho, Guimarães, Portugal, 2011.

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